Abstract
AbstractLet denote a nonempty translation invariant collection of intervals in (which we regard as a rare basis), and define the associated geometric maximal operator by We provide a sufficient condition on so that the estimate is sharp. As a corollary, we obtain sharp weak‐type estimates for maximal operators associated to several classes of rare bases including unions of one‐parameter infinite families of Córdoba, Soria, and Zygmund‐type bases.
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